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conv2.cc
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1 /*
2 
3 Copyright (C) 1999-2013 Andy Adler
4 Copyright (C) 2010 VZLU Prague
5 
6 This file is part of Octave.
7 
8 Octave is free software; you can redistribute it and/or modify it
9 under the terms of the GNU General Public License as published by the
10 Free Software Foundation; either version 3 of the License, or (at your
11 option) any later version.
12 
13 Octave is distributed in the hope that it will be useful, but WITHOUT
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
16 for more details.
17 
18 You should have received a copy of the GNU General Public License
19 along with Octave; see the file COPYING. If not, see
20 <http://www.gnu.org/licenses/>.
21 
22 */
23 
24 #ifdef HAVE_CONFIG_H
25 #include <config.h>
26 #endif
27 
28 #include "oct-convn.h"
29 
30 #include "defun.h"
31 #include "error.h"
32 #include "oct-obj.h"
33 #include "utils.h"
34 
35 enum Shape { SHAPE_FULL, SHAPE_SAME, SHAPE_VALID };
36 
37 DEFUN (conv2, args, ,
38  "-*- texinfo -*-\n\
39 @deftypefn {Built-in Function} {} conv2 (@var{A}, @var{B})\n\
40 @deftypefnx {Built-in Function} {} conv2 (@var{v1}, @var{v2}, @var{m})\n\
41 @deftypefnx {Built-in Function} {} conv2 (@dots{}, @var{shape})\n\
42 Return the 2-D convolution of @var{A} and @var{B}. The size of the result\n\
43 is determined by the optional @var{shape} argument which takes the following\n\
44 values\n\
45 \n\
46 @table @asis\n\
47 @item @var{shape} = @qcode{\"full\"}\n\
48 Return the full convolution. (default)\n\
49 \n\
50 @item @var{shape} = @qcode{\"same\"}\n\
51 Return the central part of the convolution with the same size as @var{A}.\n\
52 The central part of the convolution begins at the indices\n\
53 @code{floor ([size(@var{B})/2] + 1)}.\n\
54 \n\
55 @item @var{shape} = @qcode{\"valid\"}\n\
56 Return only the parts which do not include zero-padded edges.\n\
57 The size of the result is @code{max (size (A) - size (B) + 1, 0)}.\n\
58 @end table\n\
59 \n\
60 When the third argument is a matrix, return the convolution of the matrix\n\
61 @var{m} by the vector @var{v1} in the column direction and by the vector\n\
62 @var{v2} in the row direction.\n\
63 @seealso{conv, convn}\n\
64 @end deftypefn")
65 {
66  octave_value retval;
67  octave_value tmp;
68  int nargin = args.length ();
69  std::string shape = "full"; // default
70  bool separable = false;
71  convn_type ct;
72 
73  if (nargin < 2)
74  {
75  print_usage ();
76  return retval;
77  }
78  else if (nargin == 3)
79  {
80  if (args(2).is_string ())
81  shape = args(2).string_value ();
82  else
83  separable = true;
84  }
85  else if (nargin >= 4)
86  {
87  separable = true;
88  shape = args(3).string_value ();
89  }
90 
91  if (args(0).ndims () > 2 || args(1).ndims () > 2)
92  {
93  error ("conv2: A and B must be 1-D vectors or 2-D matrices");
94  return retval;
95  }
96 
97  if (shape == "full")
98  ct = convn_full;
99  else if (shape == "same")
100  ct = convn_same;
101  else if (shape == "valid")
102  ct = convn_valid;
103  else
104  {
105  error ("conv2: SHAPE type not valid");
106  print_usage ();
107  return retval;
108  }
109 
110  if (separable)
111  {
112  // If user requests separable, check first two params are vectors
113 
114  if (! (1 == args(0).rows () || 1 == args(0).columns ())
115  || ! (1 == args(1).rows () || 1 == args(1).columns ()))
116  {
117  print_usage ();
118  return retval;
119  }
120 
121  if (args(0).is_single_type () || args(1).is_single_type ()
122  || args(2).is_single_type ())
123  {
124  if (args(0).is_complex_type () || args(1).is_complex_type ()
125  || args(2).is_complex_type ())
126  {
127  FloatComplexMatrix a (args(2).float_complex_matrix_value ());
128  if (args(1).is_real_type () && args(2).is_real_type ())
129  {
130  FloatColumnVector v1 (args(0).float_vector_value ());
131  FloatRowVector v2 (args(1).float_vector_value ());
132  retval = convn (a, v1, v2, ct);
133  }
134  else
135  {
136  FloatComplexColumnVector v1 (args(0).float_complex_vector_value ());
137  FloatComplexRowVector v2 (args(1).float_complex_vector_value ());
138  retval = convn (a, v1, v2, ct);
139  }
140  }
141  else
142  {
143  FloatColumnVector v1 (args(0).float_vector_value ());
144  FloatRowVector v2 (args(1).float_vector_value ());
145  FloatMatrix a (args(2).float_matrix_value ());
146  retval = convn (a, v1, v2, ct);
147  }
148  }
149  else
150  {
151  if (args(0).is_complex_type () || args(1).is_complex_type ()
152  || args(2).is_complex_type ())
153  {
154  ComplexMatrix a (args(2).complex_matrix_value ());
155  if (args(1).is_real_type () && args(2).is_real_type ())
156  {
157  ColumnVector v1 (args(0).vector_value ());
158  RowVector v2 (args(1).vector_value ());
159  retval = convn (a, v1, v2, ct);
160  }
161  else
162  {
163  ComplexColumnVector v1 (args(0).complex_vector_value ());
164  ComplexRowVector v2 (args(1).complex_vector_value ());
165  retval = convn (a, v1, v2, ct);
166  }
167  }
168  else
169  {
170  ColumnVector v1 (args(0).vector_value ());
171  RowVector v2 (args(1).vector_value ());
172  Matrix a (args(2).matrix_value ());
173  retval = convn (a, v1, v2, ct);
174  }
175  }
176  } // if (separable)
177  else
178  {
179  if (args(0).is_single_type () || args(1).is_single_type ())
180  {
181  if (args(0).is_complex_type () || args(1).is_complex_type ())
182  {
183  FloatComplexMatrix a (args(0).float_complex_matrix_value ());
184  if (args(1).is_real_type ())
185  {
186  FloatMatrix b (args(1).float_matrix_value ());
187  retval = convn (a, b, ct);
188  }
189  else
190  {
191  FloatComplexMatrix b (args(1).float_complex_matrix_value ());
192  retval = convn (a, b, ct);
193  }
194  }
195  else
196  {
197  FloatMatrix a (args(0).float_matrix_value ());
198  FloatMatrix b (args(1).float_matrix_value ());
199  retval = convn (a, b, ct);
200  }
201  }
202  else
203  {
204  if (args(0).is_complex_type () || args(1).is_complex_type ())
205  {
206  ComplexMatrix a (args(0).complex_matrix_value ());
207  if (args(1).is_real_type ())
208  {
209  Matrix b (args(1).matrix_value ());
210  retval = convn (a, b, ct);
211  }
212  else
213  {
214  ComplexMatrix b (args(1).complex_matrix_value ());
215  retval = convn (a, b, ct);
216  }
217  }
218  else
219  {
220  Matrix a (args(0).matrix_value ());
221  Matrix b (args(1).matrix_value ());
222  retval = convn (a, b, ct);
223  }
224  }
225 
226  } // if (separable)
227 
228  return retval;
229 }
230 
231 /*
232 %!test
233 %! c = [0,1,2,3;1,8,12,12;4,20,24,21;7,22,25,18];
234 %! assert (conv2 ([0,1;1,2], [1,2,3;4,5,6;7,8,9]), c);
235 
236 %!test
237 %! c = single ([0,1,2,3;1,8,12,12;4,20,24,21;7,22,25,18]);
238 %! assert (conv2 (single ([0,1;1,2]), single ([1,2,3;4,5,6;7,8,9])), c);
239 
240 %!test
241 %! c = [1,4,4;5,18,16;14,48,40;19,62,48;15,48,36];
242 %! assert (conv2 (1:3, 1:2, [1,2;3,4;5,6]), c);
243 
244 %!assert (conv2 (1:3, 1:2, [1,2;3,4;5,6], "full"),
245 %! conv2 (1:3, 1:2, [1,2;3,4;5,6]));
246 
247 %% Test shapes
248 %!shared A, B, C
249 %! A = rand (3, 4);
250 %! B = rand (4);
251 %! C = conv2 (A, B);
252 %!assert (conv2 (A,B, "full"), C)
253 %!assert (conv2 (A,B, "same"), C(3:5,3:6))
254 %!assert (conv2 (A,B, "valid"), zeros (0, 1))
255 %!assert (size (conv2 (B,A, "valid")), [2 1])
256 
257 %!test
258 %! B = rand (5);
259 %! C = conv2 (A, B);
260 %!assert (conv2 (A,B, "full"), C)
261 %!assert (conv2 (A,B, "same"), C(3:5,3:6))
262 %!assert (conv2 (A,B, "valid"), zeros (0, 0))
263 %!assert (size (conv2 (B,A, "valid")), [3 2])
264 
265 %% Clear shared variables so they are not reported for tests below
266 %!shared
267 
268 %% Test cases from Bug #34893
269 %!assert (conv2 ([1:5;1:5], [1:2], "same"), [4 7 10 13 10; 4 7 10 13 10])
270 %!assert (conv2 ([1:5;1:5]', [1:2]', "same"), [4 7 10 13 10; 4 7 10 13 10]')
271 %!assert (conv2 ([1:5;1:5], [1:2], "valid"), [4 7 10 13; 4 7 10 13])
272 %!assert (conv2 ([1:5;1:5]', [1:2]', "valid"), [4 7 10 13; 4 7 10 13]')
273 
274 %!test
275 %! rand ("seed", 42);
276 %! x = rand (100);
277 %! y = ones (5);
278 %! A = conv2 (x, y)(5:end-4,5:end-4);
279 %! B = conv2 (x, y, "valid");
280 %! assert (B, A); # Yes, this test is for *exact* equivalence.
281 
282 
283 %% Test input validation
284 %!error conv2 ()
285 %!error conv2 (1)
286 %!error <must be 1-D vectors or 2-D matrices> conv2 (ones (2), ones (2,2,2))
287 %!error <SHAPE type not valid> conv2 (1,2, "NOT_A_SHAPE")
288 %% Test alternate calling form which should be 2 vectors and a matrix
289 %!error conv2 (ones (2), 1, 1)
290 %!error conv2 (1, ones (2), 1)
291 */
292 
293 DEFUN (convn, args, ,
294  "-*- texinfo -*-\n\
295 @deftypefn {Built-in Function} {@var{C} =} convn (@var{A}, @var{B})\n\
296 @deftypefnx {Built-in Function} {@var{C} =} convn (@var{A}, @var{B}, @var{shape})\n\
297 Return the n-D convolution of @var{A} and @var{B}. The size of the result\n\
298 is determined by the optional @var{shape} argument which takes the following\n\
299 values\n\
300 \n\
301 @table @asis\n\
302 @item @var{shape} = @qcode{\"full\"}\n\
303 Return the full convolution. (default)\n\
304 \n\
305 @item @var{shape} = @qcode{\"same\"}\n\
306 Return central part of the convolution with the same size as @var{A}.\n\
307 The central part of the convolution begins at the indices\n\
308 @code{floor ([size(@var{B})/2] + 1)}.\n\
309 \n\
310 @item @var{shape} = @qcode{\"valid\"}\n\
311 Return only the parts which do not include zero-padded edges.\n\
312 The size of the result is @code{max (size (A) - size (B) + 1, 0)}.\n\
313 @end table\n\
314 \n\
315 @seealso{conv2, conv}\n\
316 @end deftypefn")
317 {
318  octave_value retval;
319  octave_value tmp;
320  int nargin = args.length ();
321  std::string shape = "full"; // default
322  convn_type ct;
323 
324  if (nargin < 2 || nargin > 3)
325  {
326  print_usage ();
327  return retval;
328  }
329  else if (nargin == 3)
330  {
331  if (args(2).is_string ())
332  shape = args(2).string_value ();
333  else
334  {
335  error ("convn: SHAPE must be a string");
336  return retval;
337  }
338  }
339 
340  if (shape == "full")
341  ct = convn_full;
342  else if (shape == "same")
343  ct = convn_same;
344  else if (shape == "valid")
345  ct = convn_valid;
346  else
347  {
348  error ("convn: SHAPE type not valid");
349  print_usage ();
350  return retval;
351  }
352 
353  if (args(0).is_single_type () || args(1).is_single_type ())
354  {
355  if (args(0).is_complex_type () || args(1).is_complex_type ())
356  {
357  FloatComplexNDArray a (args(0).float_complex_array_value ());
358  if (args(1).is_real_type ())
359  {
360  FloatNDArray b (args(1).float_array_value ());
361  retval = convn (a, b, ct);
362  }
363  else
364  {
365  FloatComplexNDArray b (args(1).float_complex_array_value ());
366  retval = convn (a, b, ct);
367  }
368  }
369  else
370  {
371  FloatNDArray a (args(0).float_array_value ());
372  FloatNDArray b (args(1).float_array_value ());
373  retval = convn (a, b, ct);
374  }
375  }
376  else
377  {
378  if (args(0).is_complex_type () || args(1).is_complex_type ())
379  {
380  ComplexNDArray a (args(0).complex_array_value ());
381  if (args(1).is_real_type ())
382  {
383  NDArray b (args(1).array_value ());
384  retval = convn (a, b, ct);
385  }
386  else
387  {
388  ComplexNDArray b (args(1).complex_array_value ());
389  retval = convn (a, b, ct);
390  }
391  }
392  else
393  {
394  NDArray a (args(0).array_value ());
395  NDArray b (args(1).array_value ());
396  retval = convn (a, b, ct);
397  }
398  }
399 
400  return retval;
401 }
402 
403 /*
404 ## Check for bug #39314
405 %!test
406 %! v = reshape ([1 2], [1 1 2]);
407 %! assert (convn (v, v), reshape ([1 4 4], [1 1 3]));
408 %! assert (convn (v, v, "same"), reshape ([4 4], [1 1 2]));
409 %! assert (convn (v, v, "valid"), 4);
410 
411 ## The following test may look weird since we are using the output
412 ## of convn to test itself. However, because calculations are done
413 ## differently based on the shape option, it will help to catch some
414 ## bugs. See also bug #39314.
415 ## FIXME: The "valid" option uses an entirely different code path
416 ## through C++ and Fortran to calculate inner convolution.
417 ## The terms in the convolution added in reverse order compared
418 ## to the "full" option. This produces differences on the order
419 ## of tens of eps. This should be fixed, but in the meantime
420 ## the tests will be marked as xtests.
421 %!shared a, b, c
422 %! ## test 3D by 3D
423 %! a = rand (10, 10, 10);
424 %! b = rand (3, 3, 3);
425 %! c = convn (a, b, "full");
426 %!assert (convn (a, b, "same"), c(2:11,2:11,2:11))
427 %!xtest
428 %! assert (convn (a, b, "valid"), c(3:10,3:10,3:10));
429 %!
430 %!test
431 %! ## test 3D by 2D
432 %! a = rand (10, 10, 10);
433 %! b = rand (3, 3);
434 %! c = convn (a, b, "full");
435 %!assert (convn (a, b, "same"), c(2:11,2:11,:))
436 %!xtest
437 %! assert (convn (a, b, "valid"), c(3:10,3:10,:))
438 %!
439 %!test
440 %! ## test 2D by 3D
441 %! a = rand (10, 10);
442 %! b = rand (3, 3, 3);
443 %! c = convn (a, b, "full");
444 %!assert (convn (a, b, "same"), c(2:11,2:11,2))
445 %!assert (convn (a, b, "valid"), c(3:10,3:10,3:2)) # a 7x7x0 matrix
446 %!
447 %!test
448 %! ## test multiple different number of dimensions, with odd and even numbers
449 %! a = rand (10, 15, 7, 8, 10);
450 %! b = rand (4, 3, 2, 3);
451 %! c = convn (a, b, "full");
452 %!assert (convn (a, b, "same"), c(3:12,2:16,2:8,2:9,:))
453 %!xtest
454 %! assert (convn (a, b, "valid"), c(4:10,3:15,2:7,3:8,:))
455 
456 %!test
457 %! a = reshape (floor (magic (16) /10), [4 8 4 2]);
458 %! b = reshape (magic (6), [4 3 3]);
459 %! c = zeros (7, 10, 6, 2);
460 %! c(:,:,1,1) = [
461 %! 875 1415 1215 741 288 264 635 1109 687 171
462 %! 110 467 1551 1790 1891 1651 1165 900 659 568
463 %! 883 1047 1475 1964 2181 2302 2117 1674 579 234
464 %! 940 2330 3099 2573 2306 2207 2442 2918 2272 1004
465 %! 161 500 1564 2066 2355 2270 2099 1621 1144 831
466 %! 644 622 886 1121 1652 1967 1907 1668 529 228
467 %! 160 752 1232 768 360 284 668 1132 1380 864];
468 %! c(:,:,2,1) = [
469 %! 150 1174 1903 1971 2030 1719 1467 1420 1220 472
470 %! 986 2243 2603 2385 2308 2530 2971 3181 2266 768
471 %! 914 2443 3750 3782 3976 3821 3723 3709 2599 1178
472 %! 1922 3374 5198 5472 5563 5853 5794 5543 3578 1820
473 %! 1060 2471 3846 3724 3682 3803 3812 3927 2876 1390
474 %! 470 2078 3283 3225 2701 2265 2165 2261 2324 1124
475 %! 700 1130 1486 1515 1830 2097 2081 2028 1009 348];
476 %! c(:,:,3,1) = [
477 %! 1350 2127 2461 2082 1694 1909 2230 2621 1681 683
478 %! 877 2473 4362 4556 4543 4314 3879 3703 2863 1497
479 %! 1934 4219 5874 6117 5966 6051 5984 5714 3891 1562
480 %! 1927 5997 8573 8456 8517 8025 7957 8101 6121 2500
481 %! 1558 3533 5595 6064 6453 6491 6275 5743 3794 1832
482 %! 1950 2762 3455 3423 4019 4578 4807 4857 2304 907
483 %! 525 1860 2731 2392 1872 1724 1961 2312 2315 1141];
484 %! c(:,:,4,1) = [
485 %! 150 1317 2230 2621 2996 2767 2472 2049 1514 583
486 %! 1429 3056 3879 3703 3756 3964 4394 4570 3111 1250
487 %! 1833 4037 5984 5714 5846 5788 5883 6129 4157 2011
488 %! 3143 5469 7957 8101 8063 8475 8564 8439 5306 2538
489 %! 2001 4514 6275 5743 5391 5389 5578 6110 4473 1953
490 %! 817 3196 4807 4857 4229 3659 3477 3375 3208 1400
491 %! 750 1365 1961 2312 2840 2993 2722 2344 1092 323];
492 %! c(:,:,5,1) = [
493 %! 475 734 1296 1352 1400 1595 1557 1517 960 490
494 %! 751 1977 2831 2746 2607 2665 2733 2833 2186 912
495 %! 1065 3142 4344 4150 3768 3734 3876 4086 3366 1327
496 %! 976 3712 5530 5921 6158 5802 5481 5071 3821 1491
497 %! 1397 2996 3971 4003 4088 4180 4199 4146 2649 985
498 %! 1273 2121 2555 2247 2378 2624 2908 3229 1788 705
499 %! 365 1108 1530 1652 1550 1407 1274 1127 889 264];
500 %! c(:,:,6,1) = [
501 %! 0 133 345 683 982 1058 960 623 310 100
502 %! 437 806 1313 1332 1383 1391 1397 1370 864 495
503 %! 928 1573 2201 1928 1864 1932 2183 2445 1557 855
504 %! 1199 2083 2739 2573 2507 2656 2786 2928 1795 736
505 %! 912 1997 2404 2028 1692 1591 1803 2159 1603 599
506 %! 345 1092 1526 1666 1593 1437 1275 1116 863 253
507 %! 50 235 510 811 998 894 615 318 77 0];
508 %! c(:,:,1,2) = [
509 %! 840 1350 1176 697 293 320 674 1153 717 180
510 %! 142 490 1563 1824 1929 1604 1132 857 624 587
511 %! 890 1084 1539 1979 2238 2333 2072 1610 509 202
512 %! 966 2263 3034 2518 2250 2235 2512 2992 2305 1016
513 %! 200 561 1607 2107 2361 2277 2030 1548 1102 818
514 %! 652 631 922 1128 1670 1997 1895 1665 467 197
515 %! 160 744 1192 692 292 256 708 1208 1448 900];
516 %! c(:,:,2,2) = [
517 %! 179 1199 1886 1987 1997 1716 1479 1383 1215 485
518 %! 988 2213 2552 2358 2304 2615 3011 3210 2246 744
519 %! 921 2483 3747 3768 3960 3835 3712 3698 2588 1183
520 %! 1903 3416 5254 5490 5572 5826 5761 5505 3502 1814
521 %! 1064 2507 3825 3666 3680 3748 3821 3958 2892 1395
522 %! 495 2129 3277 3228 2566 2216 2154 2250 2390 1154
523 %! 700 1105 1472 1524 1856 2113 2059 2019 975 325];
524 %! c(:,:,3,2) = [
525 %! 1302 2104 2439 2006 1723 1931 2280 2685 1678 690
526 %! 877 2507 4408 4580 4523 4233 3852 3647 2850 1516
527 %! 1949 4238 5895 6143 6018 6063 5930 5656 3847 1538
528 %! 1953 5975 8547 8433 8407 8060 7955 8069 6170 2506
529 %! 1621 3536 5624 6117 6459 6456 6180 5666 3735 1815
530 %! 1904 2751 3429 3366 4122 4622 4840 4864 2242 882
531 %! 517 1843 2674 2337 1777 1686 2005 2367 2385 1175];
532 %! c(:,:,4,2) = [
533 %! 198 1346 2280 2685 2980 2759 2396 1982 1497 576
534 %! 1413 2994 3852 3647 3756 4035 4418 4595 3109 1231
535 %! 1873 4025 5930 5656 5792 5772 5909 6152 4185 2035
536 %! 3110 5510 7955 8069 8139 8456 8541 8439 5276 2541
537 %! 1964 4462 6180 5666 5315 5409 5631 6178 4536 1998
538 %! 869 3215 4840 4864 4121 3579 3420 3386 3271 1430
539 %! 725 1361 2005 2367 2925 3006 2667 2297 1054 325];
540 %! c(:,:,5,2) = [
541 %! 462 754 1285 1359 1441 1605 1556 1488 938 488
542 %! 729 1967 2788 2732 2608 2683 2744 2830 2195 912
543 %! 1052 3139 4302 4101 3742 3730 3895 4103 3403 1335
544 %! 1007 3725 5577 5964 6165 5754 5407 5006 3846 1507
545 %! 1375 2969 3951 3990 4144 4183 4200 4150 2661 998
546 %! 1258 2090 2495 2188 2403 2664 2954 3279 1814 723
547 %! 388 1127 1551 1673 1525 1390 1253 1139 912 275];
548 %! c(:,:,6,2) = [
549 %! 19 147 384 716 1016 1059 927 570 276 80
550 %! 441 791 1298 1320 1401 1396 1409 1367 865 500
551 %! 932 1537 2155 1870 1860 1946 2221 2487 1584 874
552 %! 1201 2067 2705 2538 2512 2687 2806 2971 1812 756
553 %! 925 1976 2363 1971 1636 1600 1844 2239 1664 626
554 %! 372 1133 1558 1687 1570 1401 1243 1122 883 264
555 %! 60 270 556 857 1024 870 569 282 66 0];
556 %!assert (convn(a, b, "full"), c)
557 %!assert (convn(a, b, "same"), c(3:6,2:9,2:5,:))
558 %!assert (convn(a, b, "valid"), c(4,3:8,3:4,:))
559 
560 ## test correct class
561 %!assert (class (convn (rand(5), rand(3))), "double")
562 %!assert (class (convn (rand(5, "single"), rand(3))), "single")
563 %!assert (class (convn (rand(5), rand(3, "single"))), "single")
564 %!assert (class (convn (true (5), rand(3))), "double")
565 %!assert (class (convn (true (5), rand(3, "single"))), "single")
566 %!assert (class (convn (ones(5, "uint8"), rand(3))), "double")
567 %!assert (class (convn (rand (3, "single"), ones(5, "uint8"))), "single")
568 
569 %!error convn ()
570 %!error convn (1)
571 %!error <SHAPE type not valid> convn (1,2, "NOT_A_SHAPE")
572 %!error convn (rand (3), 1, 1)
573 */
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